Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388998%3A_____%2F12%3A00438628" target="_blank" >RIV/61388998:_____/12:00438628 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jcp.2011.10.023" target="_blank" >http://dx.doi.org/10.1016/j.jcp.2011.10.023</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jcp.2011.10.023" target="_blank" >10.1016/j.jcp.2011.10.023</a>

Result language
angličtina
Original language name
Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods
Original language description
We present a new class of adaptivity algorithms for time-dependent partial differential equations (PDE) that combine adaptive higher-order finite elements (hp-FEM) in space with arbitrary (embedded, higher-order, implicit) Runge-Kutta methods in time. Weak formulation is only created for the stationary residual, and the Runge-Kutta methods are specified via their Butcher's tables. Around 30 Butcher's tables for various Runge-Kutta methods with numerically verified orders of local and global truncation errors are provided. A time-dependent benchmark problem with known exact solution that contains a sharp moving front is introduced, and it is used to compare the quality of seven embedded implicit higher-order Runge-Kutta methods. Numerical experiments also include a comparison of adaptive low-order FEM and hp-FEM with dynamically changing meshes. All numerical results presented in this paper were obtained using the open source library Hermes (http://www.hpfem.org/hermes) and they are rep
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
JA - Electronics and optoelectronics
OECD FORD branch
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Project
<a href="/en/project/IAA100760702" target="_blank" >IAA100760702: Methods of higher order of accuracy for solution of multi-physics coupled problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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